The Theory of Normal Form Games form the Differentiable Viewpoint

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The Theory of Normal Form Games form the Differentiable Viewpoint

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Ritzberger, Klaus

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Klaus Ritzberger

Abstract

An alternative definition of regular equilibria is introduced and shown to have the same properties as those definitions already known from the literature. The system of equations used to define regular equilibria induces a globally differentiable structure on the space of mixed strategies. Interpreting this structure as a vector field, called the Nash field, allows for a reproduction of a number of classical results from a differentiable viewpoint. Moreover, approximations of the Nash field can be used to suitably define indices of connected components of equilibria and to identify equilibrium components which are robust against small payoff perturbations.

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Publisher Info
Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 23 (1994)
Issue (Month): 3 ()
Pages: 207-36
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Handle: RePEc:spr:jogath:v:23:y:1994:i:3:p:207-36

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Yannick Viossat, 2005. "Openness of the set of games with a unique correlated equilibrium," Working Papers hal-00243016_v1, HAL. [Downloadable!]
Fabrizio Germano & Gábor Lugosi, 2004. "Global Nash Convergence of Foster and Young's Regret Testing," Economics Working Papers 788, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
Other versions:
- Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, vol. 60(1), pages 135-154, July. [Downloadable!] (restricted)
DE MICHELIS, Stefano, 2000. "On the index and asymptotic stability of dynamics," CORE Discussion Papers 2000018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
Demichelis, Stefano & Ritzberger, Klaus & Swinkels, Jeroen M., 2002. "The Simple Geometry of Perfect Information Games," Economics Series 115, Institute for Advanced Studies. [Downloadable!]
Other versions:
- Stefano Demichelis & Klaus Ritzberger & Jeroen M. Swinkels, 2004. "The simple geometry of perfect information games," International Journal of Game Theory, Springer, vol. 32(3), pages 315-338, 06. [Downloadable!] (restricted)
Ken Binmore & Larry Samuelson, . "Evolutionary Drift and Equilibrium Selection," ELSE working papers 011, ESRC Centre on Economics Learning and Social Evolution. [Downloadable!]
DE MICHELIS, Stefano & GERMANO, Fabrizio, 2000. "On the indices of zeros of nash fields," CORE Discussion Papers 2000017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
Other versions:
- Stefano DeMichelis & Fabrizio Germano, 1996. "On the Indices of Zeros of Nash Fields," University of California at San Diego, Economics Working Paper Series 96-33, Department of Economics, UC San Diego. [Downloadable!]
- DeMichelis, Stefano & Germano, Fabrizio, 2000. "On the Indices of Zeros of Nash Fields," Journal of Economic Theory, Elsevier, vol. 94(2), pages 192-217, October. [Downloadable!] (restricted)
DE MICHELIS, Stefano & GERMANO, Fabrizio, 2000. "On knots and dynamics in games," CORE Discussion Papers 2000010, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
Other versions:
- DeMichelis, S. & Germano, F., 2000. "On Knots and Dynamics in Games," Papers 2-2000, Tel Aviv.
Giuseppe De Marco & Jacqueline Morgan, 2007. "Slightly Altruistic Equilibria in Normal Form Games," CSEF Working Papers 185, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy. [Downloadable!]
DEMICHELIS, Stefano & RITZBERGER, Klaus, 2000. "From evolutionary to strategic stability," CORE Discussion Papers 2000059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
Other versions:
- Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November. [Downloadable!] (restricted)
Yannick Viossat, 2008. "Is Having a Unique Equilibrium Robust?," Post-Print hal-00361891_v1, HAL. [Downloadable!]

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